As America winds down the war, fewer sick and injured will get the top-flight U.S. medical care that for 13 years has aided Afghan soldiers and civilians.

BAGRAM AIRFIELD, Afghanistan—Keyan Riley answered the phone and reached for his green, clothbound notebook. He began scrawling notes about the two Afghan girls whose lives had just fallen into his hands. "5 yr." the doctor wrote of the younger girl. "40 mm grenade."

On the other end of the line was a surgeon from a Special Forces outpost in the Afghan hinterlands. The girls had accidentally detonated a discarded...